Related papers: An elementary construction of Anick's fibration

We verify a construction which, for $\Bbb K$ the reals, complex numbers, quaternions, or octonions, builds a spherical $t$-design by placing a spherical $t$-design on each $\Bbb K$-projective or $\Bbb K$-Hopf fiber associated to the points…

Let p be a finite regular covering on a 2-sphere with at least three branch points. In this paper, we construct a local signature for the class of fibrations whose general fibers are isomorphic to the covering p.

A hyperk\"ahler manifold $M$ has a family of induced complex structures indexed by a two-dimensional sphere $S^2 \cong \mathbb{CP}^1$. The twistor space of $M$ is a complex manifold $Tw(M)$ together with a natural holomorphic projection…

We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…

We consider the space F^E_{k,n} of all spherical tight frames of k vectors in real or complex n--dimensional Hilbert space E^n, i.e. E=R or E=C, and its orbit space G^E_{k,n}=F^E_{k,n}/O^E_n under the obvious action of the group O^E_n of…

A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore--Seiberg relations. A functor to N is constructed…

We calculate the homotopy type of the Brown-Comenetz dual $I_2$ of the K(2)-local sphere at the prime 3 and show that there is a twisting by a non-trivial element $P$ in the exotic part of the Picard group. We give a complete…

In the present paper we consider fibrations $f: S \ra B$ of an algebraic surface onto a curve $B$, with general fibre a curve of genus $g$. Our main results are: 1) A structure theorem for such fibrations in the case $g=2$ 2) A structure…

Given a conformally nonflat Einstein spacetime we define a fibration $P$ over it. The fibres of this fibration are elliptic curves (2-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the…

For a fibration with the fiber $K(\pi,n)$-space, the algebraic model as a twisted tensor product of chains of the base with standard chains of $K(\pi,n)$-complex is given which preserves multiplicative structure as well. In terms of this…

Milnor's fibration theorem and its generalizations play a central role in the study of singularities of complex and real analytic maps. In the complex analytic case, the Milnor fibration on the sphere is always given by the normalized map…

We prove fibration theorems \`a la Milnor for differentiable real maps with non isolated critical values. We study the situation for maps with linear discriminant, and prove that the concept of d-regularity is the key point for the…

We use discrete Morse theory to give a new proof of the Degree Theorem in Auter space A_n. There is a filtration of A_n into subspaces A_{n,k} using the degree of a graph, and the Degree Theorem says that each A_{n,k} is (k-1)-connected.…

We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to…

Given a $C^2$ semi-algebraic mapping $F: \mathbb{R}^N \rightarrow \mathbb{R}^p,$ we consider its restriction to $W\hookrightarrow \mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\geq p\geq 2$ and introduce…

We consider Reeb flows on the tight $3$-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition…

This note is mostly an expository survey, centered on the topology of complements of hyperplane arrangements, their Milnor fibrations, and their boundary structures. An important tool in this study is provided by the degree 1 resonance and…

We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic:…

This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…

We use Richter's $2$-primary proof of Gray's conjecture to give a homotopy decomposition of the fibre $\Omega^3S^{17}\{2\}$ of the $H$-space squaring map on the triple loop space of the $17$-sphere. This induces a splitting of the mod-$2$…